Drought Analysis under Climate Change Using Copula
Publication: Journal of Hydrologic Engineering
Volume 18, Issue 7
Abstract
The joint behavior of drought characteristics under climate change is evaluated using the copula method, which has recently attained popularity in the analysis of complex hydrologic systems with correlated variables. Trivariate copulas are applied, in this study, to analyze the major drought variables, including duration, severity, and intensity, in Oregon’s Upper Klamath River Basin. Among the variables, results show that duration severity exhibits the strongest correlation, whereas duration intensity exhibits the least correlation. The impact of climate change on future droughts is evaluated using five general circulation models (GCMs) under one emission scenario. Despite more intense extreme events that are expected to occur in most parts of the globe in the future, the results of this study show that the Upper Klamath River Basin in the Pacific Northwest will experience less intense droughts affected by climate change. Compared with historical events, an overall decrease in drought duration and severity is estimated for this study area in the time period of 2020–2090 with maximum drought duration shown to decline from 8 to 5 months. Among the five GCMs employed in this study, GFDL-CM2.1 and CSIRO-MK3.0 are identified as the wettest and driest projections, respectively. High uncertainty associated with GCM products is demonstrated in the analysis of return period by means of bivariate copulas. However, all projections result in larger return periods (i.e., less frequent droughts) compared with historical droughts during the reference period.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
We acknowledge the modeling groups, the Program for Climate Model Diagnosis and Intercomparison (PCMDI) and the WCRP’s Working Group on Coupled Modeling (WGCM) for their roles in making available the WCRP CMIP3 multimodel data set. Support of this data set is provided by the Office of Science, U.S. Department of Energy.
References
Abatzoglou, J. T., and Brown, T. J. (2011). “A comparison of statistical downscaling methods suited for wildfire applications.” Int. J. Clim., 32, 772–780.
Andreadis, K. M., and Lettenmaier, D. P. (2006). “Trends in 20th century drought over the continental United States.” Geophys. Res. Lett., 33(10), L10403.
Barros, A. P., and Bowden, G. J. (2008). “Toward long-lead operational forecasts of drought: An experimental study in the Murray-Darling River Basin.” J. Hydrol., 357(3–4), 349–367.
Blenkinsop, S., and Fowler, H. J. (2007). “Changes in drought frequency, severity and duration for the British Isles projected by the PRUDENCE regional climate models.” J. Hydrol., 342(1–2), 50–71.
Borg, D. S. (2009). “An application of drought indices in Malta, Case Study.” Eur. Water, 25/26, 25–38.
Burke, E. J., Perry, R. H. J., and Brown, S. J. (2010). “An extreme value analysis of UK drought and projections of change in the future.” J. Hydrol., 388(1–2), 131–143.
Cancelliere, A., Mauro, G. D., Bonaccorso, B., and Rossi, G. (2007). “Drought forecasting using the Standardized Precipitation Index.” Water Resour. Manage., 21(5), 801–819.
Cherubini, U., Luciano, E., and Vecchiato, W. (2004). Copula methods in finance, Wiley, Chichester, UK.
Cunderlik, J. M., and Simonovic, S. P. (2005). “Hydrological extremes in a southwestern Ontario river basin under future climate conditions [Extrêmes hydrologiques dans un basin versant du sud-ouest de l Ontario sous conditions climatiques futures].” Hydrol. Sci. J., 50(4), 631–654.
De Michele, C., Salvadori, G., Canossi, M., Petaccia, A., and Rosso, R. (2005). “Bivariate statistical approach to check adequacy of dam spillway.” J. Hydrol. Eng., 10(1), 50–57.
Dingman, S. L. (1994). Physical hydrology, Prentice Hall, Upper Saddle River, NJ.
Dracup, J. A., Lee, K. S., and Paulson, E. G., Jr. (1980). “On the definition of droughts.” Water Resour. Res., 16(2), 297–302.
Dupuis, D. J. (2007). “Using copulas in hydrology: Benefits, cautions, and issues.” J. Hydrol. Eng., 12(4), 381–393.
Dupuis, D. J. (2010). “Statistical modeling of the monthly Palmer drought severity index.” J. Hydrol. Eng., 15(10), 796–807.
Favre, A. C., Adlouni, S. E., Perreault, L., Thiéonge, N., and Bobée, B. (2004). “Multivariate hydrological frequency analysis using copulas.” Water Resour. Res., 40(1), W01101.
Federal Emergency Management Agency (FEMA). (1995). “National mitigation strategy: Partnerships for building safer communities.” Government Printing Office, Washington, DC.
Fleig, A. K., Tallaksen, L. M., Hisdal, H., and Hannah, D. M. (2011). “Regional hydrological drought in north-western Europe: Linking a new regional drought area index with weather types.” Hydrol. Processes, 25(7), 1163–1179.
Gebremichael, M., and Krajewski, W. F. (2007). “Application of copulas to modeling temporal sampling errors in satellite-derived rainfall estimates.” J. Hydrol. Eng., 12(4), 404–408.
Genest, C., Ghoudi, K., and Rivest, L. P. (1995). “A semiparametric estimation procedure of dependence parameters in multivariate families of distributions.” Biometrika, 82(3), 543–552.
Ghosh, S., and Mujumdar, P. P. (2007). “Nonparametric methods for modeling GCM and scenario uncertainty in drought assessment.” Water Resour. Res., 43(7), W07405.
Guttman, N. B. (1999). “Accepting the standardized precipitation index: A calculation algorithm.” J. Am. Water Resour. Assoc., 35(2), 311–322.
Han, P., Wang, P. X., Zhang, S. Y., and Zhu, D. H. (2010). “Drought forecasting based on the remote sensing data using ARIMA models.” Math. Comput. Model., 51(11–12), 1398–1403.
Hecht, B., and Kamman, G. (1996). “Initial assessment of pre- and post-Klamath Project hydrology on the Klamath River and impacts of the project on instream flows and fishery habitat.”, Balance Hydrologics, Inc., Berkeley, CA.
Hollinger, S. E., Isard, S. A., and Welford, M. R. (1993). “A new soil moisture drought index for predicting crop yields.” 8th Conf. on Applied Climatology, American Meteorological Society, Boston.
Intergovernmental Panel on Climate Change (IPCC). (2000). “Emissions scenarios.” Special Rep. of Working Group II, Cambridge Univ. Press, Cambridge, UK.
IPCC. (2007). “Climate change 2007: The physical science basis.” Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, Cambridge Univ. Press, Cambridge, U.K. New York.
Joe, H. (1997). “Multivariate models and dependence concept.” Chapman and Hall, New York.
Jung, I. W., Moradkhani, H., and Chang, H. (2012). “Uncertainty assessment of climate change impact for hydrologically distinct river basins.” J. Hydrol., 466–467, 73–87.
Kao, S., and Govindaraju, R. S. (2008). “Trivariate statistical analysis of extreme rainfall events via Plackett family of copulas.” Water Resour. Res., 44(2), W02415.
Kao, S, and Govindaraju, R. S. (2010). “A copula-based joint deficit index for droughts.” J. Hydrol., 380(1–2), 121–134.
Liu, W. T., and Kogan, F. N. (1996). “Monitoring regional drought using the vegetation condition index.” Int. J. Remote Sens., 17(14), 2761–2782.
Loukas, A., Vasiliades, L., and Tzabiras, J. (2008). “Climate change effects on drought severity.” Adv. Geosciences, 17, 23–29.
Luo, L., and Wood, E. F. (2007). “Monitoring and predicting the 2007 U.S. drought.” Geophys. Res. Lett., 34(22), L22702.
Maurer, E. P., Brekke, L., Pruitt, T., and Duffy, P. B. (2007). “Fine-resolution climate projections enhance regional climate change impact studies.” EOS Trans. Am. Geophys. Union, 88(47), 504.
McCabe, G. J., and Markstrom, S. L. (2007). “A monthly water-balance model driven by a graphical user interface.” U.S. Geological Survey Open-File Rep. 2007-1088, U.S. Dept. of the Interior, U.S. Geological Survey, Reston, VA.
McKee, T. B., Doesken, N. J., and Kleist, J. (1993). “The relationship of drought frequency and duration to time scales.” 8th Conf. on Applied Climatology, American Meteorological Society, Boston.
McKee, T. B., Doesken, N. J., and Kleist, J. (1995). “Drought monitoring with multiple time scales.” 9th Conf. on Applied Climatology, American Meteorological Society, Boston.
Mishra, A. K., and Singh, V. P. (2010). “A review of drought concepts.” J. Hydrol., 391(1–2), 202–216.
Moradkhani, H., Baird, R. G., and Wherry, S. (2010). “Assessment of climate change impact on floodplain and hydrologic ecotones.” J. Hydrol., 395(3–4), 264–278.
Moradkhani, H., and Meier, M. (2010). “Long-lead water supply forecast using large-scale climate predictors and independent component analysis.” J. Hydrol. Eng., 15(10), 744–762.
Najafi, M., Moradkhani, H., and Jung, I. (2011a). “Assessing the uncertainties of hydrologic model selection in climate change impact studies.” Hydrol. Processes, 25(18), 2814–2826.
Najafi, M., Moradkhani, H., and Wherry, S. (2011b). “Statistical downscaling of precipitation using machine learning with optimal predictor selection.” J. Hydrol. Eng., 16(8), 650–664.
Nalbantis, I. (2008). “Evaluation of a hydrological drought index.” Eur. Water, 23(24), 67–77.
National Aeronautics, and Space Administration (NASA). (2001). “Drought in the Klamath River Basin.” Earth Observatory, Goddard Space Flight Center, Greenbelt, MD, 〈http://earthobservatory.nasa.gov/IOTD/view.php?id=1743〉.
Nelsen, R. B. (1999). An introduction to copulas, Springer, New York.
Palmer, W. C. (1965). “Meteorologic drought.”, U.S. Dept. of Commerce, Office of Climatology, U.S. Weather Bureau, Washington, DC.
Palmer, W. C. (1968). “Keeping track of crop moisture conditions, nationwide: The new crop moisture index.” Weatherwise, 21(4), 156–161.
Risley, J., Moradkhani, H., Hay, L., and Markstrom, S. (2011). “Statistical comparisons of watershed-scale response to climate change in selected basins across the United States.” Earth Interact., 15(14), 1–26.
Salvadori, G., and De Michele, C. (2010). “Multivariate multiparameter extreme value models and return periods: A copula approach.” Water Resour. Res., 46(10), W10501.
Samadi, S. Z., Wilson, C. A., and Moradkhani, H. (2013). “Uncertainty analysis of statistical downscaling models using Hadley centre coupled model.” J. Theor. Appl. Clim., 1–18.
Serinaldi, F., and Grimaldi, S. (2007). “Fully nested 3-copula: Procedure and application on hydrological data.” J. Hydrol. Eng., 12(4), 420–430.
Shafer, B. A., and Dezman, L. E. (1982). “Development of a surface water supply index (SWSI) to assess the severity of drought conditions in snowpack runoff areas.” Western Snow Conf., Colorado State Univ., Reno, NV, 164–175.
Sheffield, J., and Wood, E. F. (2007). “Characteristics of global and regional drought, 1950–2000: Analysis of soil moisture data from off-line simulation of the terrestrial hydrologic cycle.” J. Geophys. Res., 112(17), D17115.
Sheffield, J., and Wood, E. F. (2008). “Projected changes in drought occurrence under future global warming from multi-model, multi-scenario, IPCC AR4 simulations.” Clim. Dyn., 31(1), 79–105.
Shiau, J. T. (2003). “Return period of bivariate distributed hydrological events.” Stoch. Environ. Res. Risk Assess., 17(1–2), 42–57.
Shiau, J. T. (2006). “Fitting drought duration and severity with two-dimensional copulas.” Water Resour. Manage., 20(5), 795–815.
Shiau, J. T., and Shen, H. W. (2001). “Recurrence analysis of hydrologic droughts of differing severity.” J. Water Resour. Plann. Manage., 127(1), 30–40.
Shukla, S., and Wood, A. W. (2008). “Use of a standardized runoff index 1368 for characterizing hydrologic drought.” Geophys. Res. Lett., 35(2), L02405.
Sklar, A. (1959). “Fonctions de répartition à n dimensions et leurs marges.” Publications de l’Institut de Statistique de l’Univ. de Paris, 8, 229–231.
Smakhtin, V. U. (2001). “Low flow hydrology: A review.” J. Hydrol., 240(3–4), 147–186.
Taylor, K. E., Stouffer, R. J., and Meehl, G. A. (2012). “An overview of CMIP5 and the experiment design.” Bull. Am. Meteorol. Soc., 93, 485–498.
Thornthwaite, C. W. (1948). “An approach toward a rational classification of climate.” Geogr. Rev., 38(1), 55–94.
Weghorst, K. M. (1996). “The reclamation drought index: Guidelines and practical applications.”, Bureau of Reclamation, Denver.
Wong, G., Lambert, M. F., Leonard, M., and Metcalfe, A. V. (2010). “Drought analysis using trivariate copulas conditional on climatic states.” J. Hydrol. Eng., 15(2), 129–141.
Wood, A. W., Leung, L. R., Sridhar, V., and Lettenmaier, D. P. (2004). “Hydrologic implications of dynamical and statistical approaches to downscaling climate model outputs.” Clim. Change, 62(1–3), 189–216.
Zhang, L., and Singh, V. P. (2007). “Gumbel–Hougaard copula for trivariate rainfall frequency analysis.” J. Hydrol. Eng., 12(4), 409–419.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 18 • Issue 7 • July 2013
Pages: 746 - 759
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Jun 2, 2011
Accepted: Oct 26, 2011
Published online: Oct 29, 2011
Published in print: Jul 1, 2013
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.